Unfortunately, ideal GKP states are non-normalizable states with infinite energy.
Many related methods can be used for defining finite-energy versions of these states [1]}, [2]}.
A common approximation is to replace each delta function in the GKP wave-function with a Gaussian of width \(\Delta \) , in addition to an overall Gaussian envelope of width \(1/\Delta \)  that damps the peak weighting further from the origin [3]}:
\(\begin{split}\mathinner {|{\mu ^\Delta }\rangle }_{\rm gkp} \equiv & \frac{1}{N_\mu }\int _{-\infty }^{+\infty }ds\sum _{n}e^{-\Delta ^2[(2\sqrt{\pi }+\mu )n]^2/2} \\&\hspace{42.67912pt}\times e^{-[s-(2\sqrt{\pi }+\mu )n]^2/2\Delta ^2}\mathinner {|{s}\rangle }_q,\end{split}\) 
